Input-to-state stability of nonlinear systems based on an indefinite Lyapunov function

This study investigated the input-to-state stability (ISS) and integral ISS (iISS) of nonlinear systems and discovered new sufficient conditions for them. These conditions are more relaxed than others in that they employ an indefinite Lyapunov function rather than a negative definite one. Thus, a nonlinear time-varying system satisfying them has uniform asymptotic stability. Two numerical examples show their effectiveness and advantages.